scholarly journals New Exact Solutions for an Oldroyd-B Fluid in a Porous Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
I. Khan ◽  
M. Imran ◽  
K. Fakhar
Keyword(s):  
Porous Medium ◽  
Shear Stress ◽  
Exact Solutions ◽  
Strong Influence ◽  
Stress Fields ◽  
Porous Space ◽  
New Exact Solutions ◽  
Laplace Transform Technique ◽  
Similar Solutions ◽  
Analytical Expressions

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid have been derived. The Oldroyd-B fluid saturates the porous space. Two different flow cases have been considered. The analytical expressions for velocity and shear stress fields have been obtained by using Laplace transform technique. The corresponding solutions for hydrodynamic Oldroyd-B fluid in a nonporous space appeared as the limiting cases of the obtained solutions. Similar solutions for MHD Newtonian fluid passing through a porous space are also recovered. Graphs are sketched for the pertinent parameters. It is found that the MHD and porosity parameters have strong influence on velocity and shear stress fields.

A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field

2018 ◽  
Vol 25 (3) ◽  
pp. 409-418 ◽  
Author(s):  
Amir Khan ◽  
Gul Zaman
Keyword(s):  
Shear Stress ◽  
Second Grade ◽  
Porous Space ◽  
Second Grade Fluid ◽  
New Exact Solutions ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

AbstractNew exact solutions are obtained for unsteady magnetohydrodynamic (MHD) flows of a generalized second-grade fluid near a uniform accelerating plate. The generalized second-grade fluid saturates the porous space. A fractional derivative is used in the governing equation. Analytical expressions for the velocity and shear stress fields are obtained by using the Laplace transform technique for fractional calculus. The obtained solutions are expressed in the series form in terms of Fox H-functions. Similar solutions for an ordinary second-grade fluid passing through a porous space are also derived. Moreover, several graphs are constructed for the pertinent parameters to analyze the characteristics of the velocity and shear stress field.

scholarly journals Effects of Wall Shear Stress on MHD Conjugate Flow over an Inclined Plate in a Porous Medium with Ramped Wall Temperature

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Sharidan Shafie
Keyword(s):  
Porous Medium ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Exact Solutions ◽  
Wall Temperature ◽  
Mhd Flow ◽  
Inclined Plate ◽  
Constant Wall Temperature ◽  
Laplace Transform Technique ◽  
Wall Shear

This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over an inclined plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration fields are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in detail.

scholarly journals Chemical reaction and radiation effects on unsteady MHD free convection flow in a porous medium past an infinite inclined isothermal plate

2020 ◽  
Vol 1 (01) ◽  
pp. 01-10
Author(s):  
H.I. Osman ◽  
N.F.M. Omar ◽  
D. Vieru ◽  
Z. Ismail
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Chemical Reaction ◽  
Radiation Effects ◽  
Convection Flow ◽  
Inclined Plate ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Analytical Expressions ◽  
Chemical Reaction Parameter

The effect of chemical reaction on unsteady magentohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate has been investigated. Laplace transform technique is the method to solve the solutions for velocity, temperature and concentration fields. The analytical expressions for non-dimensional skin friction, Nusselt number and Sherwood number has been presented. The influence of various embedded parameter on velocity, temperature and concentration such as chemical reaction parameter, magnetic field and radiation has been discussed in detail. The effects of involved parameters have been discussed and the numerical results are presented graphically.

scholarly journals Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Asma Khalid ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Heat And Mass Transfer ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Convection Flow ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Laplace Transform Technique

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

scholarly journals Connection between Classical Solutions of Stokes first Problem and those of Simple Couette Flow. Applications

2020 ◽  
Vol 2 (3) ◽  
pp. 1-3
Author(s):  
Constantin Fetecau ◽  
◽  
Marneni Narahari ◽  
Keyword(s):  
Shear Stress ◽  
Exact Solutions ◽  
Couette Flow ◽  
Direct Consequence ◽  
Viscous Fluids ◽  
Classical Solutions ◽  
New Exact Solutions ◽  
Constant Shear ◽  
Constant Shear Stress

The classical solutions of the first problem of Stokes for viscous fluids, as it was to be expected, are obtained as limiting cases of those of the simple Couette flow. Something similar is valid for the motions of the fluids induced by a constant shear stress on the boundary. As a direct consequence, new exact solutions are immediately obtained for other two classes of motions of the same fluids.

A Note on Exact Solutions for the Unsteady Free Convection Flow of a Jeffrey Fluid

2015 ◽  
Vol 70 (6) ◽  
pp. 397-401 ◽  
Author(s):  
Ilyas Khan
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Exact Solutions ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

AbstractIn this note, we investigate the unsteady free convection flow of a Jeffrey fluid past an infinite isothermal vertical plate. Exact solutions are obtained using the Laplace transform technique. These solutions are expressed in terms of exponential and complementary error functions, and satisfy all imposed initial and boundary conditions as well as the governing equations. The expression for the shear stress is also evaluated. The corresponding solutions for a Newtonian fluid can be easily obtained as a special case. It is found from the velocity and shear stress solutions that they strongly depend on the material parameters of a Jeffrey fluid. The exact solutions obtained here can be used as a benchmark for checking the correctness of other approximate or numerical solutions. In addition, this note will help in understanding the characteristics of non-Newtonian fluid flows that are subject to free convection due to buoyancy force.

scholarly journals Fractional magnetohydrodynamics Oldroyd-B fluid over an oscillating plate

2013 ◽  
Vol 17 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Muhammad Jamil ◽  
Alam Khan ◽  
Nazish Shahid
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Infinite Plate ◽  
Second Grade ◽  
Oscillating Flows ◽  
New Exact Solutions ◽  
Special Cases ◽  
In Series ◽  
Similar Solutions ◽  
Oscillating Plate

This paper presents some new exact solutions corresponding to the oscillating flows of a MHD Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional MHD Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox H functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary MHD Oldroyd-B, fractional and ordinary MHD Maxwell, fractional and ordinary MHD Second grade and MHD Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.

scholarly journals New Exact Solutions for MHD Transient Rotating Flow of a Second-Grade Fluid in a Porous Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Faisal Salah ◽  
Zainal Abdul Aziz ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Exact Solution ◽  
Porous Medium ◽  
Exact Solutions ◽  
Flat Plate ◽  
Laplace Transforms ◽  
Second Grade ◽  
Rotating Flow ◽  
Second Grade Fluid ◽  
New Exact Solutions ◽  
Grade Fluid

The magnetohydrodynamic (MHD) and rotating flow of second-grade fluid over a suddenly moved flat plate is investigated, where the second-grade fluid saturates the porous medium. The new exact solution is derived by using the Fourier sine and Laplace transforms. Many interesting available results in the literature are obtained as limiting cases of our solution. Finally, some graphical results are presented for different values of the material constants.

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